The electric warship is an enabling technology to enhance propulsion, add flexibility and adaptability to energy routing in the ship and to eliminate the need to carry unstable munitions through electric weapons. Pulsed loads on an electric ship are becoming more prevalent as ship component technologies move to more electric power. Many new naval loads, such as electromagnetic aircraft launch (EMAL) systems, rail-guns, lasers, and radar operate as a pulsed load when active. See A. Gattozzi et al., “Power system and energy storage models for laser integration on naval platforms,” Proc. IEEE Elect. Ship Technol. Symp., June 2015, pp. 173-180; M. Steurer et al., “Analysis of experimental rapid power transfer and fault performance in dc naval power systems,” Proc. IEEE Elect. Ship Technol. Symp., June 2015, pp. 433-440; and V. Salehi et al., “Pulse-load effects on ship power system stability,” Proc. Annu. Conf. IEEE Ind. Electron. Soc., November 2010, pp. 3353-3358. However, these pulsed loads can have a destabilizing effect on the ship's power distribution network. The electric weapon loads that are being added to electric ships are constant power when active, but are typically operated as a repetitive pulse train sequence with a power magnitude, duty cycle and period. For example, the power to a laser or an EMAL system may have a large power magnitude, but is operated in short bursts with a period of seconds. Other loads such as railguns may have periods on the order of minutes, but pulse widths in the milliseconds. Typically, these types of loads are modeled as constant power and are analyzed for stability with small-signal models and techniques. However, small-signal methods are insufficient for pulse power load stability. A typical linear Nyquist analysis may show the system is unstable for the power magnitude of the pulse, yet the method cannot accurately predict the stability of a pulse train for these loads which have nonlinear limit cycle behavior. See R. D. Robinett III and D. G. Wilson, Nonlinear Power Flow Control Design: Utilizing Exergy, Entropy, Static and Dynamic Stability, and Lyapunov Analysis, New York, N.Y., USA: Springer, 2011; R. D. Robinett III and D. G. Wilson, Int. J. Exergy 6(3), 357 (2009); and R. D. Robinett III and D. G. Wilson, Int. J. Control 81(12), 1886 (2008).
Much research has been performed on the destabilizing effects of constant power or negative impedance loads in DC systems. See R. D. Middlebrook, “Input filter considerations in design and application of switching regulators,” Proc. IEEE Ind. Appl. Soc. Annu. Meeting, 1976, pp. 366-382; W. W. Weaver and P. T. Krein, “Mitigation of power system collapse through active dynamic buffers,” Proc. IEEE Power Electron. Specialists Conf., 2004, vol. 2, pp. 1080-1084; M. N. Marwali et al., IEEE Trans. Energy Convers. 21(2), 516 (2006); M. N. Marwali et al., IEEE Trans. Energy Convers. 22(3), 737 (2007); A. Riccobono and E. Santi, IEEE Trans. Ind. Appl. 50(5), 3525 (2014); and W. Inam et al., “Stability, control, and power flow in ad hoc dc microgrids,” Proc. IEEE Workshop Control Model. Power Electron., June 2016, pp. 1-8. The general approach is to treat the constant power system as a matched impedance problem and to use linear time-invariant small-signal methods to derive solutions to mitigate the instability. See C. Wildrick et al., Trans. Power Electron. 10, 280 (1995); and S. D. Sudhoff et al., IEEE Trans. Aerosp. Electron. Syst. 36(3), 965 (2000). However, the dynamics of a pulse power load can be so dramatic that linear small-signal methods are no longer valid. A pulse power load is a time-variant system and there are linear time-variant methods such as Floquet theory. See C. A. Klausmeier, Theoretical Ecol. 1(3), 153 (2008); D. Giaouris et al., IEEE Trans. Circuits Syst. I, Reg. Papers 55(4), 1084 (2008); and J. A. Martin et al., “Exact steady state analysis in power converters using Floquet decomposition,” Proc. North Amer. Power Symp., August 2011, pp. 1-7. However, while Floquet theory addresses the time-variant nature of the pulsed load, it still fails to capture the large-signal response. Yet other methods, such as in Sanchez and Marx, address the large-signal problem but are not adequate for a pulsed load. See S. Sanchez and M. Molinas, IEEE Trans. Energy Conyers. 30(1), 122 (2015), and D. Marx et al., IEEE Trans. Power Electron. 27(4), 1773 (2012).
For DC systems with pulse power loads, the typical approach is to mitigate an instability by decoupling the load from the distribution network which requires large energy storage devices, such as flywheels, capacitors, or batteries. These energy storage devices add volume, weight, cost and reduced reliability. Most techniques used to analyze these systems are based on small-signal models, such as Nyquist, Eigenvalue or Floquet theory. However, a small-signal model is not appropriate for large pulsed power loads, and these small signal methods break down or yield inappropriate and inaccurate results. Typically, energy storage systems are used to mitigate instability of common loads based on a constant power approach. See A. Gattozzi et al., “Power system and energy storage models for laser integration on naval platforms,” Proc. IEEE Elect. Ship Technol. Symp., June 2015, pp. 173-180. However, the model of a load as constant power and not pulsed power may yield overly conservative designs and controls. See L. Domaschk et al., IEEE Trans. Magn. 43(1), 450 (2007). If the system design allows for a nonlinear limit cycle driven by a pulsed load then less energy storage may be necessary.